Hence, the existential predecessors are symbolically represented by !(c|!a), i.e., !c&a which are the states s6:{a,b} and s4:{a}, and yes, indeed, these are the only two states having a transition towards the green states.

If you enter as state set predicate b<->(c->b) and select existential predecessors, your problem will be solved by the tool.

The above operation is very important for symbolic model checking, and is usually carried out using BDDs for the formulas. In that case, special BDD algorithms will compute the state set directly as a BDD.